Answer:
The probability of selling three cars next week is approximately 0.0733, or 7.33%.
Explanation:
We can use the Poisson distribution to solve this problem, since it models the number of events (in this case, the number of cars sold) that occur in a fixed period of time, given a known rate of occurrence.
The Poisson distribution has the following formula:
P(x) = (e^(-λ) * λ^x) / x!
where:
- P(x) is the probability of x events occurring
- e is the mathematical constant (approximately equal to 2.71828)
- λ is the average rate of occurrence
- x is the number of events that we want to calculate the probability for
- x! is the factorial of x (i.e., x! = x * (x-1) * (x-2) * ... * 2 * 1)
In this case, we know that the rate of occurrence (λ) is 1.1 cars per week, and we want to calculate the probability of selling 3 cars (x = 3) next week. Substituting these values into the Poisson distribution formula, we get:
P(3) = (e^(-1.1) * 1.1^3) / 3!
P(3) = (0.332871 * 1.331) / 6
P(3) = 0.0733
Therefore, the probability of selling three cars next week is approximately 0.0733, or 7.33%.